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Determinante von $$$\left[\begin{array}{cc}\cosh{\left(t \right)} & 1\\\sinh{\left(t \right)} & 0\end{array}\right]$$$
Verwandter Rechner: Kofaktormatrix-Rechner
Ihre Eingabe
Berechne $$$\left|\begin{array}{cc}\cosh{\left(t \right)} & 1\\\sinh{\left(t \right)} & 0\end{array}\right|$$$.
Lösung
Die Determinante einer 2x2-Matrix ist $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.
$$$\left|\begin{array}{cc}\cosh{\left(t \right)} & 1\\\sinh{\left(t \right)} & 0\end{array}\right| = \left(\cosh{\left(t \right)}\right)\cdot \left(0\right) - \left(1\right)\cdot \left(\sinh{\left(t \right)}\right) = - \sinh{\left(t \right)}$$$
Antwort
$$$\left|\begin{array}{cc}\cosh{\left(t \right)} & 1\\\sinh{\left(t \right)} & 0\end{array}\right| = - \sinh{\left(t \right)}$$$A